In this verse, Paul challenged us to refrain from any "strife" or "vainglory"--words that seem a bit stern in the colloquial terms of our day.
Eritheia is the Greek word for "strife"--a contentious political maneuvering for greater power. "Vainglory" is similar. It comes from the Greek word kenodoxia, an empty pride or groundless glory. Both are rather unpleasant descriptions of the foolish and sinful human behavior that is seen all too often among God’s people: "Let us not be desirous of vain glory, provoking one another, envying one another" (Galatians 5:26).
On the contrary, we are challenged to "esteem" the others in our fellowship as "better than" ourselves. The precise words in this instruction insist that we are to use deliberate and careful judgment in our evaluation of others in our relationships as being more "excellent" than what we have thought of ourselves.
Now that goes against most of what we have been taught in our Western educational systems. Self-esteem is de rigueur in our schools, songs, movies, and television programs. In fact "positive thinking" and "prosperity thinking" are very little more than self-esteem dressed up in religious terms.
In the biblical "body" analogy, we are told that "those members of the body, which we think to be less honourable, upon these we bestow more abundant honour . . . having given more abundant honour to that part which lacked" (1 Corinthians 12:23-24).
God thinks differently. We are told to think of each other like God thinks. HMM III http://www.icr.org/article/esteem-others/